JPH11279759A - Sputtering shape simulation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a sputtering shape simulation method capable of shortening a calculation time. SOLUTION: The three-dimensional particle orbits calculated by a Monte Carlo method are sorted at a two-dimensionally projected angle and the shape calculation is executed by selecting the particle orbits exclusive of the particles at which shadows occur definitely from the angle formed with a horizontal axial direction of a shadow decision point in the sputtering shape simulation method in a semiconductor process. Pseudo three-dimensional shadow decision is carried out only with respect to the selected particle orbits.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a sputtering shape simulation method for simulating a shape of a film formed on a semiconductor substrate by sputtering in a sputtering process in a semiconductor device manufacturing process.

[0002]

2. Description of the Related Art An example of a conventional sputtering shape simulation method is disclosed in JP-A-09-015101 and JP-A-09-015101.
SISPAD96 Tec published by Japan Society of Applied Physics in 1996
"A Pract, published on pages 77-78 of hnicalDigest
ical Sputter Equipment Simulation System for Alumi
H.Ya entitled "num Including Surface Diffusion Model"
It is described in a paper by mada.

FIG. 3 is a diagram showing this conventional sputtering shape simulation method. This simulation method includes means for directing the flux to the shape, means for determining whether the flux is shadowed, and means for moving the shape point when the flux is not shadowed.

[0004] The conventional sputtering shape simulation system having such a configuration operates as follows.
That is, from the trajectory of the sputtered particles calculated by the Monte Carlo method, pseudo three-dimensional shadow determination is performed as follows to calculate the film growth. First, string data is created by connecting each coordinate point of the outline obtained by cutting at the center line of the contact hole, and the contact hole shape is modeled.
From the coordinate points constituting the shape, one coordinate point for which film growth is to be calculated is selected, and the trajectory of the sputtered particle calculated by the Monte Carlo method is directed to that point. One shape point for shadow determination is selected, and the distance between this point and the axis of symmetry of the contact hole is calculated. Calculate the intersection between the horizontal plane and the trajectory including the shape point to determine the shadow, and when the distance between the intersection and the contact hole symmetry axis is larger than the distance between the shape point to determine the shadow and the contact hole symmetry axis,
It is assumed that particles do not enter due to the shadow effect. If the shadow effect does not occur, the scoring point whose film growth is to be calculated is moved in the incident direction of the orbit. Said ~
The shadow judgment is performed for all the shape points by the operation of.
The film growth is calculated at all the shape points by the above-mentioned operations.

[0005]

However, in this prior art, even if most of the sputtered particles do not contribute to the film growth due to the shadow, the shadow determination is performed for all the trajectories of the sputtered particles.
There is a problem that it takes a lot of calculation time to determine whether or not the Monte Carlo particles contribute to the film growth. In addition to the above publications, JP-A-6-52269,
JP-A-8-171549, JP-A-8-27408
No. 4 discloses a shape simulation method, but these known techniques also have a disadvantage that a long calculation time is required.

The present invention has been made in view of such a problem, and an object of the present invention is to provide a sputtering shape simulation method capable of shortening a calculation time.

[0007]

According to the present invention, there is provided a method for simulating a sputter shape in a method of simulating a sputter shape in a semiconductor process, wherein a three-dimensional particle trajectory calculated by a Monte Carlo method is sorted at an angle projected two-dimensionally. A step of selecting shapes other than particles that clearly cause a shadow from an angle between the horizontal axis direction of the shadow determination point and a shape calculation, and a step of performing pseudo three-dimensional shadow determination only on the selected particle trajectory. I do.

According to another sputtering shape simulation method according to the present invention, a trajectory of a sputtered particle calculated by the Monte Carlo method is projected on the XZ plane, and the angle θx formed by the X axis is sorted in ascending order. Projecting the trajectory of the sputtered particles on the YZ plane and sorting them in ascending order of the angle θy with the Y axis, and creating string data connecting each coordinate point of the outline obtained by cutting the contact hole center line on the XZ plane Modeling the shape of the contact hole, calculating the angle θ at which the straight line connecting the coordinate point growing on the YZ plane and the upper end of the base shape forms the Y-axis, and θ3 ≦ from the trajectory of the sputtered particles. θy ≦
selecting a trajectory of the sputtered particles to be π−θ3;
Selecting one coordinate point for determining shadow and calculating a distance R between the point and a contact hole symmetry axis;
An angle θ1 between a straight line connecting the shape point growing on the plane and the shape point for determining the shadow to the X-axis, and a straight line connecting an axis-symmetric point between the growing shape point and the shape point for determining the shadow to the X-axis. Calculating the angle θ2, selecting the trajectory of the sputtered particles such that θ1 ≦ θx ≦ θ2, directing one of the selected sputtered particles to a coordinate point where the film growth is to be calculated, Calculating a distance r between the intersection of the horizontal plane containing the coordinate point to be determined and the trajectory of the sputtered particle and the symmetry axis; When the distance r between the intersection of the orbits and the symmetry axis is large, the film growth is not calculated, and when r <R, the coordinate point for calculating the film growth is moved in the incident direction of the orbit to calculate the film growth. And having Features.

[0009]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be specifically described below with reference to the accompanying drawings. FIGS. 1 and 2 are flow charts showing a method of the first embodiment of the present invention. FIGS. 3 and 4 are two-dimensional cross-sectional views of the via hole in the XZ plane. FIGS. 5 and 6 are schematic diagrams of projection data of the orbits of the sputtered particles calculated by the Monte Carlo method on the XZ plane and the YZ plane, respectively. It is a schematic diagram of pseudo three-dimensional shadow determination.

First, the trajectories of sputtered particles calculated by the Monte Carlo method are projected on the XZ plane, and sorted in ascending order of the angle θx with the X axis (step 101). That is, the trajectories of the sputtered particles calculated by the Monte Carlo method are sorted according to the angle θx formed by the projection on the XZ plane with the X axis. The three-dimensional trajectory of the sputtered particle, calculated by the Monte Carlo method, is projected onto the XZ plane. And the unit vector in the X-axis direction Is calculated by the following equation (1).

[0011]

(Equation 1)

After calculating the angles θx for all the trajectories, sorting is performed in ascending order, numbers are assigned in ascending order, and the numbers are stored in an array. That is, one of the orbit data of the sputtered particles is randomly selected, θx is stored in the data array, and 1 is substituted into the variable N and 1 into the variable M, respectively. Next, the angle θx of the trajectory of the next sputtered particle is compared with the value of θx of the N-th data. Equation 4 below is applied to odd M. On the other hand, when the angle θx of the trajectory of the sputtered particles is smaller than the value of θx of the N-th data, the total number of data equal to or less than N is set as a new M, and Equation 3 is applied to the even M, and the odd M is Equation 5
And calculate a new N.

[0013]

N = N + ２ × M

[0014]

[Equation 3] N = N-1 / 2 × M

[0015]

N = N + ／ × (M−1)

[0016]

N = N−1 / 2 × (M−1) This is continued until M = 1. If the data is larger than N at that time, between N and N + 1, If smaller, the data of the next sputtered particle is stored just before N. Through the above procedure, all sputtered particles are stored in the data array in ascending order of θx.

Next, the trajectory of the sputtered particles calculated by the Monte Carlo method is projected on the YZ plane, and the angle θy formed with the Y axis is obtained.
Are sorted in ascending order (step 102). That is, the trajectories of the sputtered particles calculated by the Monte Carlo method are sorted according to the angle formed by the projection on the YZ plane with the Y axis. The vector projected on the YZ plane of the three-dimensional trajectory is And the unit vector in the Y-axis direction Is calculated by Equation 6 below.

[0018]

(Equation 6)

After calculating the angles θy for all the trajectories, sorting is performed in ascending order, numbers are assigned in ascending order, and the numbers are stored in an array. The sorting procedure at this time is exactly the same as the sorting procedure of θx using Equations 2 to 4.

Thereafter, string data is created on the XZ plane in the wafer radial direction and connecting each coordinate point of the outline obtained by cutting at the center line of the contact hole, and the shape of the contact hole is modeled (step 103). That is, the sectional shape of the contact hole in the XZ plane is modeled. String data connecting each coordinate point of an outline obtained by cutting along a contact hole center line included in the XZ plane as shown in FIG. 7 is created, and the contact hole shape is modeled.

Then, one of the coordinate points whose film growth is to be calculated is selected from the coordinate points forming the shape shown in FIG. 7 (step 104).

Next, an angle θ3 between a straight line connecting the shape point for film growth and the upper end of the base shape to the Y axis on the YZ plane is calculated (step 105). That is, on the YZ plane, the angle formed by the straight line connecting the coordinate point for growing the film and the upper end of the base shape to the Y axis is calculated. As shown in FIG. 4, on the YZ plane,
Starting from the coordinate point for film growth, a vector heading toward the upper end point of the base And the unit vector in the Y-axis direction is The angle θ3 is calculated by the following equation (7).

[0023]

(Equation 7)

Next, from the trajectory of the sputtered particles, θ3 ≦
The trajectory of the sputtered particles that satisfies θy ≦ π−θ3 is selected (step 106). That is, the trajectory of the sputtered particle having θy of θ3 or more and π−θ3 or less is selected. As shown in FIG. 6, from the trajectory data of the sputtered particles sorted on the YZ plane, particles whose θy is equal to or larger than θ3 and equal to or smaller than π−θ3 are selected by binary sorting. Specifically, in the same procedure as when θy is sorted using Equations 2 to 5, the position of the projection data of the sputtered particles of θ3 on the YZ plane is specified on the array in which the projection data is sorted by θy, and θy is determined. ≧ θ3, the number of data in which θy is closest to θ3 is Nmin, and θx ≦
π-θ3, the number of data in which θy is closest to θ3 is Nmax, and the stored number N is Nmin <N <Nma
By selecting the data of x, the trajectory of the sputtered particles that satisfies θ3 ≦ θx ≦ π−θ3 is selected. If θy <θ3 or θy> π−θ3 for all particles, it is assumed that shadow occurs for all particles.

Next, one coordinate point for shadow determination is selected, and the distance R between this point and the contact hole symmetry axis is calculated (step 107). As shown in FIG. 7, one coordinate point (Xshadow, 0, Zshadow) for shadow determination is selected, and the distance R between this point and the symmetry axis (0,0, Zshadow) of the contact hole is calculated by the following equation (8).

[0026]

R ² = Xshadow ² Then, on the XZ plane, the angle θ1 between the X axis and the straight line connecting the growing shape point and the shape point for determining the shadow, and the shape for determining the growing shape point and the shadow An angle θ2 between a straight line connecting the points that are axially symmetrical and the X axis is calculated (step 108). That is, on the XZ plane, the angle formed by the straight line connecting the coordinate point for film growth, the coordinate point for determining the shadow, and the axis symmetrical point of the coordinate point for determining the shadow to the X axis is calculated. As shown in FIG. 3, a vector headed from a point to be grown to a point to be subjected to shadow determination is defined as a vector. And the unit vector in the X-axis direction is The angle θ1 is obtained by the following equation (9). Further, starting from the coordinate point for growing the film, a vector heading toward an axis-symmetric point to the coordinate point for determining the shadow is obtained. And the unit vector in the X-axis direction is The angle θ2 is calculated by the following equation (10).

[0027]

(Equation 9)

[0028]

(Equation 10)

Next, the trajectory of the sputtered particles satisfying θ1 ≦ θx ≦ θ2 is selected (step 109). As shown in FIG. 5, from the trajectory data of the sputtered particles sorted on the XZ plane, particles having θx of θ1 or more and θ2 or less are selected by binary sorting. That is, θ3 ≦ θx ≦ θ
The trajectory of the sputtered particles satisfying θ1 ≦ θx ≦ θ2 is selected in the same procedure as when the trajectory of the sputtered particle 3 is selected.

Next, one of the selected sputtered particles is directed to a coordinate point at which film growth is to be calculated (step 110).

Next, the distance r between the intersection of the trajectory of the sputtered particle and the horizontal plane containing the coordinate point for shadow determination and the axis of symmetry is calculated (step 111). That is, the distance r between the trajectory of the sputtered particle on the shadow determination surface and the axis of symmetry is calculated. More specifically, as shown in FIG. 7, intersections (Xcr, Yc, Z
cr) is calculated, and the square of the distance r between the intersection and the contact hole symmetry axis (0, 0, Zcr) is calculated by the following equation (11).

[0032]

R ² = Xcr ² + Ycr ^{2 When} the distance r between the intersection point of the shadow determination surface and the orbit of the sputtered particle and the symmetry axis is larger than the distance R between the coordinate point for shadow determination and the symmetry axis of the contact hole. It is determined that the film growth is not calculated assuming that the shadow effect occurs (step 112). That is, when r is greater than the distance R between the shape point to be determined to be shadowed and the axis of symmetry of the contact hole, a pseudo three-dimensional shadow determination is made that no particles are incident due to the shadow effect.

When no shadow effect occurs, that is, when r <
In the case of R, the film growth is calculated by moving the coordinate point where the film growth is to be calculated in the incident direction of the orbit (step 113). That is, when no shadow effect occurs,
The coordinate point for which the film growth is to be calculated is moved in the incident direction of the orbit, and the film growth is calculated.

Steps 110 to 113
By the above operation, pseudo quasi three-dimensional shadow judgment is performed when the shadow effect occurs for all the selected orbits of the sputtered particles, and when the shadow effect does not occur, the film growth is calculated (step 114).

Further, shadow determination is performed on the coordinate points constituting all the shapes by the operations of steps 107 to 113 (step 115).

In this way, the film growth is calculated at the coordinate points constituting all the shapes by the operations of steps 104 to 113 (step 116).

In this embodiment, a three-dimensional sputtered particle trajectory is projected on a two-dimensional plane, and a particle which is clearly shadowed is two-dimensionally determined as a shadow. Since the number of times of shadow determination is reduced, for example, a sputtered particle having a cos distribution has an aspect ratio of 2 which expresses a shape at coordinate points at half the height.
16% of the sputtered particles that reach the coordinate point at the bottom of the contact hole, 49% of those that reach the coordinate point at half the height of the contact hole, and the coordinate point at the top of the contact hole Can be selected before performing pseudo three-dimensional shadow determination. For this reason, the calculation time for the pseudo three-dimensional shadow determination proportional to the number of particles is 55%.
((16 + 49 + 100) / (100 + 100 + 10
0) × 100). Thus, the calculation time required for the pseudo three-dimensional shadow determination can be reduced to about half.

Next, a second embodiment of the present invention will be described with reference to FIG.
This will be described with reference to FIG. In the present embodiment, first, when the trajectories of the sputtered particles extracted by the Monte Carlo method are sorted, grouping is performed so that the number of trajectory data in each range is about 10% of the whole.

Next, when specifying a range sandwiched between θmin and θmax used in performing shadow determination of two-dimensional data, first, a group min and a group max including θmin and θmax are specified. On this occasion,
The group to be symmetric is determined at the boundary of the group specified in the previous shadow determination of the film growth point, and when out of the range, the group is determined to be in the adjacent group specified last time.

Further, binary sorting of θmin in the group min and θmax in the group max is performed, respectively, to determine the positions of the data of θmin and θmax. Hereinafter, as in the first embodiment, the film growth is calculated using the orbit data of the selected sputtered particles.

The effect peculiar to the second embodiment is, for example, 10
In the case of binary sorting of 00 data in the first embodiment, ten determinations are required. However, in the second embodiment, two determinations are made for a group and seven determinations are made for a group. 9 times, the positions of θmin and θmax can be specified, and the data of θmin ≦ θ ≦ θmax can be selected. The calculation time required for binary sorting is reduced to 90%, and the calculation time required for binary sorting is reduced If it is set to 10%, the total calculation time can be reduced by 1%. This is because, when sorting is performed by angle, it is divided into groups including about 10% of the total, and when searching for the position of θ,
This is because the calculation is performed using only the groups before and after the previous selection.

[0042]

As described above, according to the present invention,
The three-dimensional sputtered particle trajectory is projected onto a two-dimensional plane, and the particles that are clearly shadowed are determined two-dimensionally as shadows.
Since the number of times of the three-dimensional shadow determination that requires a calculation time is reduced in proportion to the number of particles, the calculation time required for the pseudo three-dimensional shadow determination can be significantly reduced.

[Brief description of the drawings]

FIG. 1 is a flowchart showing the first half of a method according to a first embodiment of the present invention.

FIG. 2 is a flowchart showing the latter half of the method according to the first embodiment of the present invention.

FIG. 3 is a two-dimensional cross-sectional view of a via hole.

FIG. 4 is a two-dimensional sectional view of the via hole.

FIG. 5 is a schematic diagram of projection data of a trajectory of a sputtered particle onto a two-dimensional plane.

FIG. 6 is a schematic diagram of projection data of a trajectory of a sputtered particle onto a two-dimensional plane.

FIG. 7 is a schematic diagram of pseudo three-dimensional shadow determination.

FIG. 8 is a schematic diagram showing projection data of a trajectory of a sputtered particle onto a two-dimensional plane in the method according to the second embodiment of the present invention.

[Description of Signs] 101 to 116: Step

Claims (2)

[Claims] 1. A method for simulating a sputter shape in a semiconductor process, wherein a step of sorting a three-dimensional particle trajectory calculated by a Monte Carlo method at an angle projected two-dimensionally, and an angle between a shadow determination point and a horizontal axis direction are clarified. A sputter shape simulation method comprising: a step of selecting and calculating a shape other than particles in which a shadow occurs; and a step of performing pseudo three-dimensional shadow determination only on a selected particle orbit. 2. A step of projecting the trajectory of the sputtered particle calculated by the Monte Carlo method on the XZ plane, sorting the trajectory of the sputtered particle calculated by the Monte Carlo method on the YZ plane, and sorting the trajectory of the sputtered particle calculated by the Monte Carlo method in ascending order. , A step of sorting in ascending order of the angle θy with the Y axis, a step of creating string data connecting each coordinate point of an outline obtained by cutting the contact hole center line on the XZ plane, and modeling the contact hole shape. Calculating the angle θ formed by the straight line connecting the coordinate point growing on the YZ plane and the upper end of the base shape to the Y axis, and calculating the angle θ3 ≦ θy ≦
selecting a trajectory of the sputtered particles to be π−θ3;
Selecting one coordinate point for determining shadow and calculating a distance R between the point and a contact hole symmetry axis;
An angle θ1 between a straight line connecting the shape point growing on the plane and the shape point for determining the shadow to the X-axis, and a straight line connecting an axis-symmetric point between the growing shape point and the shape point for determining the shadow to the X-axis. Calculating the angle θ2, selecting the trajectory of the sputtered particles such that θ1 ≦ θx ≦ θ2, directing one of the selected sputtered particles to a coordinate point where the film growth is to be calculated, Calculating a distance r between the intersection of the horizontal plane containing the coordinate point to be determined and the trajectory of the sputtered particle and the symmetry axis; When the distance r between the intersection of the orbits and the symmetry axis is large, the film growth is not calculated, and when r <R, the coordinate point for calculating the film growth is moved in the incident direction of the orbit to calculate the film growth. And having Characteristic sputtering shape simulation method.